 1.3.1: Fill in the blank(s) to correctly complete each sentence. The Pytha...
 1.3.2: Fill in the blank(s) to correctly complete each sentence. In the de...
 1.3.3: Fill in the blank(s) to correctly complete each sentence. For any n...
 1.3.4: Fill in the blank(s) to correctly complete each sentence. If cot u ...
 1.3.5: Fill in the blank(s) to correctly complete each sentence. If the te...
 1.3.6: Fill in the blank(s) to correctly complete each sentence. If a quad...
 1.3.7: The terminal side of an angle u in standard position passes through...
 1.3.8: The terminal side of an angle u in standard position passes through...
 1.3.9: The terminal side of an angle u in standard position passes through...
 1.3.10: The terminal side of an angle u in standard position passes through...
 1.3.11: Sketch an angle u in standard position such that u has the least po...
 1.3.12: Sketch an angle u in standard position such that u has the least po...
 1.3.13: Sketch an angle u in standard position such that u has the least po...
 1.3.14: Sketch an angle u in standard position such that u has the least po...
 1.3.15: Sketch an angle u in standard position such that u has the least po...
 1.3.16: Sketch an angle u in standard position such that u has the least po...
 1.3.17: Sketch an angle u in standard position such that u has the least po...
 1.3.18: Sketch an angle u in standard position such that u has the least po...
 1.3.19: Sketch an angle u in standard position such that u has the least po...
 1.3.20: Sketch an angle u in standard position such that u has the least po...
 1.3.21: Sketch an angle u in standard position such that u has the least po...
 1.3.22: Sketch an angle u in standard position such that u has the least po...
 1.3.23: Sketch an angle u in standard position such that u has the least po...
 1.3.24: Sketch an angle u in standard position such that u has the least po...
 1.3.25: Sketch an angle u in standard position such that u has the least po...
 1.3.26: Sketch an angle u in standard position such that u has the least po...
 1.3.27: Sketch an angle u in standard position such that u has the least po...
 1.3.28: Sketch an angle u in standard position such that u has the least po...
 1.3.29: Sketch an angle u in standard position such that u has the least po...
 1.3.30: Sketch an angle u in standard position such that u has the least po...
 1.3.31: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.32: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.33: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.34: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.35: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.36: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.37: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.38: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.39: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.40: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.41: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.42: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.43: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.44: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.45: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.46: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.47: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.48: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.49: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.50: Suppose that the point 1x, y2 is in the indicated quadrant. Determi...
 1.3.51: An equation of the terminal side of an angle u in standard position...
 1.3.52: An equation of the terminal side of an angle u in standard position...
 1.3.53: An equation of the terminal side of an angle u in standard position...
 1.3.54: An equation of the terminal side of an angle u in standard position...
 1.3.55: An equation of the terminal side of an angle u in standard position...
 1.3.56: An equation of the terminal side of an angle u in standard position...
 1.3.57: An equation of the terminal side of an angle u in standard position...
 1.3.58: An equation of the terminal side of an angle u in standard position...
 1.3.59: An equation of the terminal side of an angle u in standard position...
 1.3.60: An equation of the terminal side of an angle u in standard position...
 1.3.61: An equation of the terminal side of an angle u in standard position...
 1.3.62: An equation of the terminal side of an angle u in standard position...
 1.3.63: Find the indicated function value. If it is undefined, say so. See ...
 1.3.64: Find the indicated function value. If it is undefined, say so. See ...
 1.3.65: Find the indicated function value. If it is undefined, say so. See ...
 1.3.66: Find the indicated function value. If it is undefined, say so. See ...
 1.3.67: Find the indicated function value. If it is undefined, say so. See ...
 1.3.68: Find the indicated function value. If it is undefined, say so. See ...
 1.3.69: Find the indicated function value. If it is undefined, say so. See ...
 1.3.70: Find the indicated function value. If it is undefined, say so. See ...
 1.3.71: Find the indicated function value. If it is undefined, say so. See ...
 1.3.72: Find the indicated function value. If it is undefined, say so. See ...
 1.3.73: Find the indicated function value. If it is undefined, say so. See ...
 1.3.74: Find the indicated function value. If it is undefined, say so. See ...
 1.3.75: Find the indicated function value. If it is undefined, say so. See ...
 1.3.76: Find the indicated function value. If it is undefined, say so. See ...
 1.3.77: Find the indicated function value. If it is undefined, say so. See ...
 1.3.78: Find the indicated function value. If it is undefined, say so. See ...
 1.3.79: Find the indicated function value. If it is undefined, say so. See ...
 1.3.80: Find the indicated function value. If it is undefined, say so. See ...
 1.3.81: Find the indicated function value. If it is undefined, say so. See ...
 1.3.82: Find the indicated function value. If it is undefined, say so. See ...
 1.3.83: Find the indicated function value. If it is undefined, say so. See ...
 1.3.84: How can the answer to Exercise 83 be given once the answers to Exer...
 1.3.85: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.86: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.87: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.88: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.89: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.90: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.91: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.92: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.93: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.94: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.95: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.96: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.97: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.98: Use trigonometric function values of quadrantal angles to evaluate ...
 1.3.99: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.100: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.101: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.102: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.103: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.104: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.105: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.106: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.107: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.108: If n is an integer, n # 180 represents an integer multiple of 180, ...
 1.3.109: In later chapters we will study trigonometric functions of angles o...
 1.3.110: In later chapters we will study trigonometric functions of angles o...
 1.3.111: In later chapters we will study trigonometric functions of angles o...
 1.3.112: In later chapters we will study trigonometric functions of angles o...
 1.3.113: Set a TI graphing calculator to parametric and degree modes. Use th...
 1.3.114: Set a TI graphing calculator to parametric and degree modes. Use th...
 1.3.115: Set a TI graphing calculator to parametric and degree modes. Use th...
 1.3.116: Set a TI graphing calculator to parametric and degree modes. Use th...
 1.3.117: Set a TI graphing calculator to parametric and degree modes. Use th...
 1.3.118: Set a TI graphing calculator to parametric and degree modes. Use th...
Solutions for Chapter 1.3: Trigonometric Functions
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 1.3: Trigonometric Functions
Get Full SolutionsChapter 1.3: Trigonometric Functions includes 118 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 11. Trigonometry was written by and is associated to the ISBN: 9780134217437. Since 118 problems in chapter 1.3: Trigonometric Functions have been answered, more than 22654 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)ยท(b  Ax) = o.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.